For Ice Cream:
Bring 1 cup cream, half and half, and 1/2 cup sugar just to simmer in medium saucepan.
Whisk yolks; gradually whisk in cream mixture. Return mixture to saucepan. Stir over medium heat until custard thickens, about 4 minutes (do not boil). Strain into bowl.
Refrigerate custard until cold, about 3 hours.
Place peaches, corn syrup, and 1/4 cup sugar in medium saucepan. Stir over medium heat until peaches are heated through, about 4 minutes. Mash to coarse puree. Cool completely. Stir into custard along with vanilla and 1/2 cup cream. Process custard in ice cream maker according to manufacturer's instructions.
Mix all ingredients. Let stand 10 minutes and up to 1 hour, tossing occasionally. Serve ice cream with compote.
Adapted from Bon Appétit August 2002